This symposium, held at Innsbruck/lgls on June 21-26, 1987, is the fifth in a series of IUTAM-Symposia on the application of stochastic methods in mechanics. The flrst two meetings in Warwick (1972) and Southhampton (1976) concentrated on the stability of stochastic dynamical systems and stochastic methods in dynamics, respectively. The third meeting in Frankfurt/Oder (1982) added aspects of reliability, while the fourth symposium in Stockholm (1984) dealt mainly with fatigue and fracture problems. The general theme of the present symposium is devoted to nonlinear stochastic dynamics of engineering systems which is believed of great importance for providing the tools for basic development and progress in various fields of mechanical-, structural- and aeronautical engineering, particularly in the areas of vehicle dynamics, multi-storey structural dynamics, systems identiflcation, offshore structural dynamics, nuclear structures under various stochastic loading conditions (i. e. wind-, earthquake-, parametric excitations, etc. ). The contributions collected in this volume cover a wide spectrum of topics ranging from more theoretical, analytical and numerical treatment to practical application in various flelds. The truly international character of the meeting is accomplished by 42 contributions and 86 participants from as many as 19 countries and hence, contributed to the original idea of IUTAM, which is to foster international cooperation. It should be recalled, that, for getting this cooperation started again after the First World War, Theodore von Kanmm and Tullio Levi-Civita called the world's flrst international (IUTAM) conference on hydro- and aerornechanics in 1922 in Innsbruck, Austria.

The Symposium, held in Torino (lSI, Villa Gualino) July 1-5, 1991 is the sixth of a series of IUTAM-Symposia on the application of stochastic analysis to continuum and discrete mechanics. The previous one, held in Innsbruck (1987), was mainly concentrated on qual itative and quantitative analysis of stochastic dynamical systems as well as on bifurcation and transition to chaos of deterministic systems. This Symposium concentrated on fundamental aspects (stochastic analysis and mathe matical methods), on specific applications in various branches of mechanics, engineering and applied sciences as well as on related fields as analysis of large systems, system identifica tion, earthquake prediction. Numerical methods suitable to provide quantitative results, say stochastic finite elements, approximation of probability distribution and direct integration of differential equations have also been the object of interesting presentations. Specific topics of the sessions have been: Engineering Applications, Equivalent Lineariza tion of Discrete Stochastic Systems, Fatigue and Life Estimation, Fluid Dynamics, Numerical Methods, Random Vibration, Reliability Analysis, Stochastic Differential Equations, System Identification, Stochastic Control. We are indebted to the IUTAM Bureau for having promoted and sponsored this Sympo sium and the Scientific Committee for having collaborated to the selection of participants and lecturers as well as to a prompt reviewing of the papers submitted for publication into these proceedings. A special thank is due to Frank Kozin: the organization of this meeting was for him ';ery important; he missed the meeting but his organizer ability was present.

Engineering systems have played a crucial role in stimulating many of the modern developments in nonlinear and stochastic dynamics. After 20 years of rapid progress in these areas, this book provides an overview of the current state of nonlinear modeling and analysis for mechanical and structural systems. This volume is a coherent compendium written by leading experts from the United States, Canada, Western and Eastern Europe, and Australia. The 22 articles describe the background, recent developments, applications, and future directions in bifurcation theory, chaos, perturbation methods, stochastic stability, stochastic flows, random vibrations, reliability, disordered systems, earthquake engineering, and numerics. The book gives readers a sophisticated toolbox that will allow them to tackle modeling problems in mechanical systems that use stochastic and nonlinear dynamics ideas. An extensive bibliography and index ensure this volume will remain a reference standard for years to come.

For most cases of interest, exact solutions to nonlinear equations describing stochastic dynamical systems are not available. This book details the relatively simple and popular linearization techniques available, covering theory as well as application. It examines models with continuous external and parametric excitations, those that cover the majority of known approaches.

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

This book contains some new developments in the area of Structural Dynamics. In general it reflects the recent efforts of several Austrian research groups during the years 1985 - 1990. The contents of this book cover both theoretical developments as well as practical applications and hence can be utilized by researchers as well as the practicing engineers. Quite naturally, realistic modeling of a number of load types such as wind and earthquake loading, etc. , requires taking into account statistical uncertainties. Hence these loads have to be characterized by stochastic processes. As a consequence, stochastic aspects must play a major role in modem structural dynamics. Since an extended modeling of the load processes should not be counterbalanced by simplifying the structural models, considerable efforts have been put into the development of procedures which allow the utilization of e. g. FE models and codes which are utilized presently in context with simplified, i. e. "deterministic" load models. Thus the processing of the additional information on loads as well as including statistical properties of the material allows to provide additional answers, i. e. quantification of the risk of structural failure. This volume concentrates on four major areas, i. e. on load modeling, structural response analysis, computational reliability procedures, and finally on practical application. Quite naturally only special fields and particular, i. e. selected types of problems can be covered. Specific reference is made, however, to cases where generalizations are possible.

This is a systematic presentation of several classes of analytical techniques in non-linear random vibration. The book also includes a concise treatment of Markovian and non-Markovian solutions of non-linear differential equations.